All categories

2 years ago

The difference in ages between a father and a son is 35. The sum is

Mathematics

2 answers:

kenny6666 [7]2 years ago

7 0

66

Difference means subtract. So, 101-35=66

katrin2010 [14]2 years ago

4 0

66. You need to subtract

You might be interested in

Arrange these functions from the greatest to the least value based on the average rate of change in the specific interval

oee [108]

The average r. of c. of a function f(x) on an interval [a,b] is:

f(b) - f(a)
--------------
b-a

You'll need to apply this to all four of the given functions.

First function: f(x) = x^2 + 3x
a= -2; b= 3

Then the ave. r. of c. for this function on this interval is:

18 - (-2) 20
------------------ = ---------- = 4. y increases by 4 for every unit increase in x.
3-(-2) 5

Do the same thing for the other 3 functions.

Then arrange your four results in descending order (greatest to least).

5 0

3 years ago

The sum of a number and 20 is no more than the sum of the square of the number and 9.

aniked [119]

A is the correct answer.

break down the word problem.

You also have to recognize key words which figure into mathematical symbols.

ex. sum of a number and 20 is x+20

square of the number and 9 is (x+9)^2

please vote my answer brainliest! thanks.

5 0

3 years ago

What is 20% of 1630?

sveticcg [70]

20% = 0.20.2 * 1630 = 326

4 0

3 years ago

Read 2 more answers

Please solve, answer choices included.

qaws [65]

4. To solve this problem, we divide the two expressions step by step:

$\frac{x+2}{x-1}* \frac{x^{2}+4x-5 }{x+4}$
Here we have inverted the second term since division is just multiplying the inverse of the term.

$\frac{x+2}{x-1}* \frac{(x+5)(x-1)}{x+4}$
In this step we factor out the quadratic equation.

$\frac{x+2}{1}* \frac{(x+5)}{x+4}$
Then, we cancel out the like term which is x-1.

We then solve for the final combined expression:
$\frac{(x+2)(x+5)}{(x+4)}$

For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:

$x-1\neq0$
$x+5\neq0$
$x+4\neq0$

Therefore, x should not be equal to 1, -5, or -4.

Comparing these to the choices, we can tell the correct answer.

ANSWER: $\frac{(x+2)(x+5)}{(x+4)}$ ; $x\neq1,-4,-5$

5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:

$\frac{ \frac{1}{3} \pi r^{2}h }{ \pi r^{2}+ \pi r \sqrt{ r^{2} +h^{2} } }$

We can simplify this expression by factoring out the denominator and cancelling like terms.

$\frac{ \frac{1}{3} \pi r^{2}h }{ \pi r(r+ \sqrt{ r^{2} +h^{2} } )}$
$\frac{ rh }{ 3(r+ \sqrt{ r^{2} +h^{2} } )}$
$\frac{ rh }{ 3r+ 3\sqrt{ r^{2} +h^{2} } }$

We then rationalize the denominator:

$\frac{rh}{3r+3 \sqrt{ r^{2} + h^{2} }} * \frac{3r-3 \sqrt{ r^{2} + h^{2} }}{3r-3 \sqrt{ r^{2} + h^{2} }}$
$\frac{rh(3r-3 \sqrt{ r^{2} + h^{2} })}{(3r)^{2}-(3 \sqrt{ r^{2} + h^{2} })^{2}}}=\frac{3 r^{2}h -3rh \sqrt{ r^{2} + h^{2} }}{9r^{2} -9 (r^{2} + h^{2} )}=\frac{3rh(r -\sqrt{ r^{2} + h^{2} })}{9[r^{2} -(r^{2} + h^{2} )]}=\frac{rh(r -\sqrt{ r^{2} + h^{2} })}{3[r^{2} -(r^{2} + h^{2} )]}$

Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:

$\frac{r*r(r -\sqrt{ r^{2} + r^{2} })}{3[r^{2} -(r^{2} + r^{2} )]}=\frac{ r^{2} (r -\sqrt{2 r^{2} })}{3[r^{2} -(2r^{2} )]}=\frac{ r^{2} (r -r\sqrt{2 })}{-3r^{2} }=\frac{r -r\sqrt{2 }}{-3 }=\frac{r(1 -\sqrt{2 })}{-3 }$

By examining the choices, we can see one option similar to the answer.

ANSWER: $\frac{r(1 -\sqrt{2 })}{-3 }$

8 0

3 years ago

Please help its confusing meeeeee

GaryK [48]

Answer:

Step-by-step explanation:

Apply the Pythagorean Theorem to solve for the length of p.